Formula Of Angle Bisector

Angle Bisector Formula (Trigonometry):

\[ \tan\left(\frac{\theta}{2}\right) = \frac{\text{opposite}}{\text{adjacent}} \]

tan(θ/2):

Opposite/Adjacent:

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1. What is the Angle Bisector Formula?

Definition: This formula relates the tangent of half an angle to the ratio of the opposite side to the adjacent side in a right triangle.

Purpose: It helps in trigonometry and geometry to find angle bisector properties and solve triangle-related problems.

2. How Does the Formula Work?

The formula is:

\[ \tan\left(\frac{\theta}{2}\right) = \frac{\text{opposite}}{\text{adjacent}} \]

Where:

\( \theta \) — The angle in degrees
opposite — Length of the side opposite to the angle
adjacent — Length of the side adjacent to the angle

Explanation: The tangent of half the angle equals the ratio of the opposite side to the adjacent side in a right triangle.

3. Importance of Angle Bisector

Details: Angle bisectors are crucial in geometry for dividing angles into two equal parts, solving triangle problems, and in various construction applications.

4. Using the Calculator

Tips: Enter the angle in degrees (0-360°), opposite side length, and adjacent side length. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: Can the angle be greater than 360°?
A: No, the calculator accepts angles between 0° and 360°.

Q2: What if the adjacent side is zero?
A: The adjacent side cannot be zero as it would make the ratio undefined.

Q3: How accurate are the results?
A: Results are accurate to 6 decimal places for precise calculations.

Q4: Can this be used for non-right triangles?
A: The formula specifically applies to right triangles. For other triangles, different angle bisector formulas apply.

Q5: What's the practical application of this formula?
A: It's used in navigation, construction, engineering, and computer graphics where angle division is needed.